Bioturbation and erosion rates along the soil-hillslope conveyor belt, part 2: Quantification using an analytical solution of the diffusion-advection equation

Particles on soil-mantled hillslopes are subject to downslope transport by erosion processes and vertical mixing by bioturbation. Both are key processes for understanding landscape evolution and soil formation, and affect the functioning of the critical zone. We show here how the depth-age information, derived from feldspar-based single grain post-infrared infrared stimulated luminescence (pIRIR), can be used to simultaneously quantify erosion and bioturbation processes along a hillslope. In this study, we propose, for the first time, an analytical solution for the diffusion-advection equation to calculate the diffusivity constant and erosion-deposition rates. We have fitted this model to age-depth data derived from 15 soil samples from four soil profiles along a catena located under natural grassland in the Santa Clotilde Critical Zone Observatory, in the south of Spain. A global sensitivity analysis was used to assess the relative importance of each model parameter in the output. Finally, the posterior probability density functions were calculated to evaluate the uncertainty in the model parameter estimates. The results show that the diffusivity constant at the surface varies from 11.4 to 81.9 mm(2) a(-1) for the hilltop and hill-base profile, respectively, and between 7.4 and 64.8 mm(2) a(-1) at 50 cm depth. The uncertainty in the estimation of the erosion-deposition rates was found to be too high to make a reliable estimate, probably because erosion-deposition processes are much slower than bioturbation processes in this environment. This is confirmed by a global sensitivity analysis that shows how the most important parameters controlling the age-depth structure in this environment are the diffusivity constant and regolith depth. Finally, we have found a good agreement between the soil reworking rates proposed by earlier studies, considering only particle age and depth, and the estimated diffusivity constants. The soil reworking rates are effective rates, corrected for the proportion of particles actually participating in the process. (c) 2019 John Wiley & Sons, Ltd.